We report a new visual illusion, where a global shape appears to continually move away from fixation, even though it remains a fixed distance from fixation. The illusion occurs because local motion signals within the object indicate motion away from fixation, and are incorrectly attributed by the visual system to the motion trajectory of the global object. A simple weighted vector summation of global and local motion signals, while a reasonable first approximation, cannot fully account for our data. We show that the faster the local motion signal, the more it biases judgments of global motion direction. We propose that local and global motion signals are summed non-linearly for this stimulus because as local motion speed increases, moving luminance blobs are visible for less time, affording less time to inhibit inappropriate component motion signals. This effect reveals the degree to which the visual system can incorrectly combine local and global motion signals belonging to a single object.